The teaching of intelligent design would not be a violation of the First amendment (BTW, ES, the Constitution was the second attempt at a unifying set of laws, the Articles of Confederation came first) as the first amendment states:

Amendment I

Congress shall make no law respecting an establishment of religion, or prohibiting the free exercise thereof; or abridging the freedom of speech, or of the press; or the right of the people peaceably to assemble, and to petition the government for a redress of grievances.

respecting an establishment of religion, ie no more Church of England. The idea of separation of church and state actually came from a letter written by Jefferson well after the writing of the Constitution.
Intelligent design as stated does not state that a particular deity created everything, just points out that that is one theory of how we got here.